Question: $ \left(\dfrac{1}{16}\right)^{-\frac{7}{4}}$
Explanation: $= 16^{\frac{7}{4}}$ $= \left(16^{\frac{1}{4}}\right)^{7}$ To simplify $16^{\frac{1}{4}}$ , figure out what goes in the blank: $\left(? \right)^{4}=16$ To simplify $16^{\frac{1}{4}}$ , figure out what goes in the blank: $\left({2}\right)^{4}=16$ so $ 16^{\frac{1}{4}}=2$ So $16^{\frac{7}{4}}=\left(16^{\frac{1}{4}}\right)^{7}=2^{7}$ $= 2\cdot2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$ $= 4\cdot2\cdot 2\cdot 2\cdot 2\cdot 2$ $= 8\cdot2\cdot 2\cdot 2\cdot 2$ $= 16\cdot2\cdot 2\cdot 2$ $= 32\cdot2\cdot 2$ $= 64\cdot2$ $= 128$